Dimensional-invariance principles in coupled dynamical systems : A unified analysis and applications
(2019) In IEEE Transactions on Automatic Control 64(8). p.3514-3520- Abstract
In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on collinear dynamical systems and their variations are discussed recently by Montenbruck et. al. in [1], while in this paper we aim to provide a unified analysis to derive the dimensional-invariance principles for networked coupled systems, and to generalize the invariance principles for networked systems with more general forms of coupling terms. To be specific, we consider two types of coupled systems, one with scalar couplings and the other with matrix couplings. Via the rank-preserving flow theory, we show that any scalar-coupled dynamical system (with constant,... (More)
In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on collinear dynamical systems and their variations are discussed recently by Montenbruck et. al. in [1], while in this paper we aim to provide a unified analysis to derive the dimensional-invariance principles for networked coupled systems, and to generalize the invariance principles for networked systems with more general forms of coupling terms. To be specific, we consider two types of coupled systems, one with scalar couplings and the other with matrix couplings. Via the rank-preserving flow theory, we show that any scalar-coupled dynamical system (with constant, time-varying or state-dependent couplings) possesses the dimensional-invariance principles, in that the dimension of the subspace spanned by the individual systems' solutions remains invariant. For coupled dynamical systems with matrix coefficients/couplings, necessary and sufficient conditions (for constant, time-varying and state-dependent couplings) are given to characterize dimensional-invariance principles. The proofs via a rank-preserving matrix flow theory in this paper simplify the analysis in [1], and we also extend the invariance principles to the cases of time-varying couplings and statedependent couplings. Furthermore, subspace-preserving property and signature-preserving flows are also developed for coupled networked systems with particular coupling terms. These invariance principles provide insightful characterizations to analyze transient behaviors and solution evolutions for a large family of coupled systems, such as multi-agent consensus dynamics, distributed coordination systems, formation control systems, among others.
(Less)
- author
- Sun, Zhiyong LU and Yu, Changbin Brad
- organization
- publishing date
- 2019
- type
- Contribution to journal
- publication status
- published
- subject
- in
- IEEE Transactions on Automatic Control
- volume
- 64
- issue
- 8
- pages
- 3514 - 3520
- publisher
- IEEE - Institute of Electrical and Electronics Engineers Inc.
- external identifiers
-
- scopus:85057403867
- ISSN
- 0018-9286
- DOI
- 10.1109/TAC.2018.2883373
- language
- English
- LU publication?
- yes
- id
- 6fa23d03-1f82-43d0-a74d-6e01d7dc8d92
- date added to LUP
- 2018-12-10 12:35:27
- date last changed
- 2022-04-25 19:40:35
@article{6fa23d03-1f82-43d0-a74d-6e01d7dc8d92,
abstract = {{<p>In this paper we study coupled dynamical systems and investigate dimension properties of the subspace spanned by solutions of each individual system. Relevant problems on collinear dynamical systems and their variations are discussed recently by Montenbruck et. al. in [1], while in this paper we aim to provide a unified analysis to derive the dimensional-invariance principles for networked coupled systems, and to generalize the invariance principles for networked systems with more general forms of coupling terms. To be specific, we consider two types of coupled systems, one with scalar couplings and the other with matrix couplings. Via the rank-preserving flow theory, we show that any scalar-coupled dynamical system (with constant, time-varying or state-dependent couplings) possesses the dimensional-invariance principles, in that the dimension of the subspace spanned by the individual systems' solutions remains invariant. For coupled dynamical systems with matrix coefficients/couplings, necessary and sufficient conditions (for constant, time-varying and state-dependent couplings) are given to characterize dimensional-invariance principles. The proofs via a rank-preserving matrix flow theory in this paper simplify the analysis in [1], and we also extend the invariance principles to the cases of time-varying couplings and statedependent couplings. Furthermore, subspace-preserving property and signature-preserving flows are also developed for coupled networked systems with particular coupling terms. These invariance principles provide insightful characterizations to analyze transient behaviors and solution evolutions for a large family of coupled systems, such as multi-agent consensus dynamics, distributed coordination systems, formation control systems, among others.</p>}},
author = {{Sun, Zhiyong and Yu, Changbin Brad}},
issn = {{0018-9286}},
language = {{eng}},
number = {{8}},
pages = {{3514--3520}},
publisher = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
series = {{IEEE Transactions on Automatic Control}},
title = {{Dimensional-invariance principles in coupled dynamical systems : A unified analysis and applications}},
url = {{http://dx.doi.org/10.1109/TAC.2018.2883373}},
doi = {{10.1109/TAC.2018.2883373}},
volume = {{64}},
year = {{2019}},
}